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A determinant formula from random walks
Archivum mathematicum, Tome 59 (2023) no. 5, pp. 421-431 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute the determinant of a large class of matrices. Two examples involving digraphs and hyperplane arrangements are provided.
One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute the determinant of a large class of matrices. Two examples involving digraphs and hyperplane arrangements are provided.
DOI : 10.5817/AM2023-5-421
Classification : 05B20, 15A15, 60C05, 60J10
Keywords: random walk; stochastic matrix; distance function; determinant 
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Randriamaro, Hery. A determinant formula from random walks. Archivum mathematicum, Tome 59 (2023) no. 5, pp. 421-431. doi: 10.5817/AM2023-5-421

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